In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our approach is a combination between a multiobjective method and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC (Difference of Convex) programming and DC algorithm. A numerical example is included for illustration.
Keywords: Multiobjective programming, stochastic programming, DCA, DC programming, utility function, expected value criterion
@article{RO_2021__55_4_2413_0,
author = {Kasri, Ramzi and Bellahcene, Fatima},
title = {A novel approach for solving stochastic problems with multiple objective functions},
journal = {RAIRO. Operations Research},
pages = {2413--2422},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {4},
doi = {10.1051/ro/2021112},
mrnumber = {4303672},
zbl = {1479.90146},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021112/}
}
TY - JOUR AU - Kasri, Ramzi AU - Bellahcene, Fatima TI - A novel approach for solving stochastic problems with multiple objective functions JO - RAIRO. Operations Research PY - 2021 SP - 2413 EP - 2422 VL - 55 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021112/ DO - 10.1051/ro/2021112 LA - en ID - RO_2021__55_4_2413_0 ER -
%0 Journal Article %A Kasri, Ramzi %A Bellahcene, Fatima %T A novel approach for solving stochastic problems with multiple objective functions %J RAIRO. Operations Research %D 2021 %P 2413-2422 %V 55 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021112/ %R 10.1051/ro/2021112 %G en %F RO_2021__55_4_2413_0
Kasri, Ramzi; Bellahcene, Fatima. A novel approach for solving stochastic problems with multiple objective functions. RAIRO. Operations Research, Tome 55 (2021) no. 4, pp. 2413-2422. doi: 10.1051/ro/2021112
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